| # | ODE | Mathematica | Maple | Sympy |
| \[
{} \left ({\mathrm e}^{2 y}+x \right ) {y^{\prime }}^{3}+y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 2 y^{\prime }+4 {y^{\prime }}^{3}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} a {y^{\prime }}^{3}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = x {y^{\prime }}^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (a x +b y\right ) {y^{\prime }}^{3}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a y \left (1+{y^{\prime }}^{2}\right )^{2}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = a \left (x y^{\prime }-y\right )^{k}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} g \left (x \right ) y^{\prime }+f \left (x \right ) {y^{\prime }}^{k}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = A \,x^{a} y^{b} {y^{\prime }}^{c}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = a \sqrt {b y^{2}+{y^{\prime }}^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = a y {\left (1+\left (b -y^{\prime }\right )^{2}\right )}^{{3}/{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = a \left (b +c x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{3} y^{\prime }+y^{\prime \prime } = y y^{\prime } \sqrt {y^{4}+4 y^{\prime }}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = f \left (y^{\prime }\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = f \left (a x +b y, y^{\prime }\right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime } = f \left (x , \frac {y^{\prime }}{y}\right ) y
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime } = x^{n -2} f \left (y x^{-n}, x^{-n +1} y^{\prime }\right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 2 y^{\prime \prime } = y \left (a -y^{2}\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 9 {y^{\prime }}^{4}+8 y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} a \,{\mathrm e}^{y} x +y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{5}+2 y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{n}+2 y^{\prime }+x y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{m} y^{n}+2 y^{\prime }+x y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} a \,x^{m} y^{n}+2 y^{\prime }+x y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} b \,{\mathrm e}^{y} x +a y^{\prime }+x y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (-x^{2} a +2\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime } = \left (1-y\right ) y^{\prime }
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x {y^{\prime }}^{2}+x y^{\prime \prime } = y^{\prime }
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime } = x {y^{\prime }}^{2}+y^{\prime }
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -2 y^{\prime }+2 x {y^{\prime }}^{2}+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime } = -y^{2}-2 y^{\prime }+x^{2} {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime } = {y^{\prime }}^{3}+y^{\prime }
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 y^{\prime }+x y^{\prime \prime } = a \,x^{2 k} {y^{\prime }}^{k}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }+{y^{\prime }}^{3}+2 x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} a y \left (1-y^{n}\right )+x^{2} y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} a \,{\mathrm e}^{y-1}+x^{2} y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (a +1\right ) x y^{\prime }+x^{2} y^{\prime \prime } = x^{k} f \left (x^{k} y, k y+x y^{\prime }\right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} {y^{\prime }}^{2}+x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime } = \left (3 x -2 y^{\prime }\right ) y^{\prime }
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime } = 6 y-4 x^{2} y^{2}+x^{4} {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime } = \sqrt {b y^{2}+a \,x^{2} {y^{\prime }}^{2}}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime } = f \left (\frac {x y^{\prime }}{y}\right ) y
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 2 y+a y^{3}+9 x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{3} y^{\prime \prime } = a \left (x y^{\prime }-y\right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{4} y^{\prime \prime } = -4 y^{2}+x \left (x^{2}+2 y\right ) y^{\prime }
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{4} y^{\prime \prime } = -4 y^{2}+x^{2} y^{\prime } \left (x +y^{\prime }\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x y^{\prime }-y\right )^{3}+x^{4} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{b}+x^{a} y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \sqrt {x}\, y^{\prime \prime } = y^{{3}/{2}}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{{3}/{2}} y^{\prime \prime } = f \left (\frac {y}{\sqrt {x}}\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} f \left (x \right ) f^{\prime }\left (x \right ) y^{\prime }+f \left (x \right )^{2} y^{\prime \prime } = g \left (y, f \left (x \right ) y^{\prime }\right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 2 f \left (x \right )^{2} y^{\prime \prime } = 2 f \left (x \right )^{2} y^{3}+f \left (x \right ) y^{2} f^{\prime }\left (x \right )+f \left (x \right ) \left (-2 f \left (x \right ) y+3 f^{\prime }\left (x \right )\right ) y^{\prime }+y \left (-2 f \left (x \right )^{3}-2 {f^{\prime }\left (x \right )}^{2}+f \left (x \right ) f^{\prime \prime }\left (x \right )\right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{2}+{y^{\prime }}^{2}+y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 a^{2} y^{2}+{y^{\prime }}^{2}+y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = y y^{\prime }+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = {\mathrm e}^{x} y \left (\operatorname {a0} +\operatorname {a1} y^{2}\right )+{\mathrm e}^{2 x} \left (\operatorname {a2} +\operatorname {a3} y^{4}\right )+{y^{\prime }}^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime \prime } = \ln \left (y\right ) y^{2}+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = -x^{2} y^{2}+\ln \left (y\right ) y^{2}+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = y^{\prime }
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = -y^{\prime }+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = y^{2} \left (f \left (x \right ) y+g^{\prime }\left (x \right )\right )+y^{\prime }+{y^{\prime }}^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime \prime } = -2 y^{\prime }+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y-x y^{\prime }+{y^{\prime }}^{2}+y y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} a x y^{\prime }+{y^{\prime }}^{2}+y y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime \prime } = y^{3}-f^{\prime }\left (x \right ) y+f \left (x \right ) y^{\prime }+{y^{\prime }}^{2}
\]
|
✓ |
✗ |
✗ |
|
| \[
{} y y^{\prime \prime } = -f \left (x \right ) y^{3}+y^{4}-f \left (x \right ) y^{\prime }+{y^{\prime }}^{2}+y f^{\prime \prime }\left (x \right )
\]
|
✓ |
✗ |
✗ |
|
| \[
{} y y^{\prime \prime } = -b y^{2}-a y y^{\prime }+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = b y^{2}+y^{3}+a y y^{\prime }+{y^{\prime }}^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime \prime } = y^{2} y^{\prime }+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = g \left (x \right ) y^{2}+f \left (x \right ) y y^{\prime }+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = -y \left (f^{\prime }\left (x \right )-y^{2} g^{\prime }\left (x \right )\right )+\left (f \left (x \right )+g \left (x \right ) y^{2}\right ) y^{\prime }+{y^{\prime }}^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime \prime } = 2 {y^{\prime }}^{2}+y^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = -2 y^{2}+2 {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = y^{2}-3 y y^{\prime }+3 {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = a {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = b y^{3}+a {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = c y^{2}+b y y^{\prime }+a {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = \operatorname {a2} y^{2}+\operatorname {a3} y^{a +1}+\operatorname {a1} y y^{\prime }+a {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} g \left (x \right ) y^{2}+f \left (x \right ) y y^{\prime }+a {y^{\prime }}^{2}+y y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} {y^{\prime }}^{3}+y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = {y^{\prime }}^{2} \left (1-y^{\prime } \sin \left (y\right )-\cos \left (y\right ) y y^{\prime }\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 {y^{\prime }}^{2}+\left (1-y\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a +y\right ) y^{\prime \prime } = {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b {y^{\prime }}^{2}+\left (a +y\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y^{\prime }+{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y^{\prime } \left (1+y^{\prime }\right )+\left (x -y\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x -y\right ) y^{\prime \prime } = \left (1+y^{\prime }\right ) \left (1+{y^{\prime }}^{2}\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x -y\right ) y^{\prime \prime } = f \left (y^{\prime }\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y y^{\prime \prime } = {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y y^{\prime \prime } = 8 y^{3}+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y y^{\prime \prime } = 4 y^{2}+8 y^{3}+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y y^{\prime \prime } = 4 y^{2} \left (2 y+x \right )+{y^{\prime }}^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 2 y y^{\prime \prime } = y^{2} \left (b y+a \right )+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|